CN106483374B - A Harmonic Interharmonic Detection Method Based on Nuttall Double-window All-phase FFT - Google Patents
A Harmonic Interharmonic Detection Method Based on Nuttall Double-window All-phase FFT Download PDFInfo
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Abstract
The present invention relates to a kind of harmonic wave harmonic detection methods based on Nuttall double window whole phase FFT.The presence of harmonic wave and m-Acetyl chlorophosphonazo brings huge harm to electric system in power grid, there are some problems in terms of spectrum leakage inhibition and phase-detection for traditional Fast Fourier Transform (FFT) FFT transform algorithm, to improve measurement accuracy, invention introduces all phase Fourier analysis (the all-phase FFT for inhibiting function with phase invariant characteristic and good spectrum leakage, apFFT), and in conjunction with the Nuttall window good with sidelobe performance, the amplitude and frequency of detection are corrected using FFT/apFFT phase difference correction method again afterwards, realize the detection of Harmonious Waves in Power Systems m-Acetyl chlorophosphonazo.The present invention has a clear superiority in terms of spectrum leakage inhibition and phase-detection, and compared with conventional method, the present invention has better precision.Still there is preferable robustness and reliability in the case where Complex Power harmonic detecting especially includes m-Acetyl chlorophosphonazo.
Description
Technical field
The present invention relates to electric power quality technical fields, especially a kind of to be based on Nuttall double window whole phase FFT
Harmonic wave harmonic detection method.
Background technique
With the development of smart grid, the access of various new energies such as wind energy, solar energy, biological energy source, cause harmonic wave and
M-Acetyl chlorophosphonazo, which has become, influences power quality and an important factor for power grid security, how high-precision detection harmonic wave m-Acetyl chlorophosphonazo and to eliminate
Its influence is inhibited to have become one of important subject of power domain.Currently, harmonic wave and m-Acetyl chlorophosphonazo detection are mainly by quick
Fourier transformation (Fast Flourier Transform, FFT) is completed, but in the case where non-synchronous sampling, due to fence
Effect and spectrum leakage problem, detection accuracy will receive serious influence, and research finds new method to carry out measurement of correlation
Just become extremely important.
In view of the above problems, domestic and foreign scholars have done many researchs, in existing method, windows and interpolated FFT is that one kind is answered
With more extensive algorithm, what is more early proposed is bispectrum line window function and interpolation algorithm, rear to have three spectral line window function and interpolation algorithms etc. again.?
In existing window function, Nuttall window is preferably a kind of window function of the more effect of Recent study.Nuttall window is a kind of
Cosine combination window, side lobe peak level is small and the progressive rate of decay of secondary lobe is big, can inhibit to close on leakage well and far from letting out
Leakage.
In recent years, information processing research field proposes a kind of signal for inhibiting function with good phases characteristic and leakage
Parser, i.e. all phase FFT spectrum analysis.At present all phase FFT spectrum analysis have application to Frequency Estimation, power quality analysis and from
The many aspects such as dynamic quasi-synchronization paralleling.In frequency analysis field, since traditional Interpolating Window FFT Algorithm is there are still correction of complex,
The problems such as phase measurement is not accurate enough, all phase analysis is also introduced frequency analysis by some researchs at present, these researchs are to humorous
Good thinking is provided in the detection of wave and m-Acetyl chlorophosphonazo, but is worth in the completeness of algorithm and considering also for precision into one
Walk the place improved.
Summary of the invention
The purpose of the present invention is to provide a kind of harmonic wave harmonic detection method based on Nuttall double window whole phase FFT,
Both the better 43 rank Nuttall windows of sidelobe performance are combined by the algorithm with all phase Fourier algorithm, combine
Advantage, error caused by spectrum leakage when on the one hand reducing detection, on the other hand improves the precision of phase-detection；Afterwards again
Testing result is corrected in conjunction with the bearing calibration of FFT/apFFT, and then obtains accurate analysis result；Add compared to tradition
Window interpolation algorithm, this algorithm apply harmonic wave m-Acetyl chlorophosphonazo detection in precision it is higher, robustness and reliability are more preferably.
To achieve the above object, the technical scheme is that a kind of harmonic wave based on Nuttall double window whole phase FFT
Harmonic detection method will inhibit the side of all phase FFT spectrum analysis of function with phase invariant characteristic and good spectrum leakage
Method, it is rear using between traditional FFT algorithm and all phase Fourier algorithm apFFT in conjunction with the Nuttall window good with sidelobe performance
Connection, is corrected using amplitude and frequency of the FFT/apFFT phase difference correction method to detection, between realization Harmonious Waves in Power Systems
Harmonic detecting.
In an embodiment of the present invention, the specific implementation steps are as follows for this method,
Step S1: acquiring the signal analyzed from power grid, if the discrete-time signal containing harmonic wave that sampling obtains
Are as follows:
In formula: h is overtone order, and H is highest subharmonic, f1For fundamental frequency, fsFor sample frequency, such as sampling thheorem institute
It states: twice of highest frequency component in the presence of sample frequency is higher than signal in value, Ah、θhRespectively h subharmonic
Virtual value and phase angle；
Step S2: it is collected to upper step as a result, take the primary data of 2N-1 point, by 43 rank Nuttall windows into
The first weighting of row, Nuttall window is as a kind of cosine combination window, time-domain expression are as follows:
In formula: M is the item number of window function；N=0,1,2 ..., N-1；bmConstraint condition should be met, For 43 rank Nuttall windows, b0-b3Take 0.338946 respectively, 0.481973,0.161054,
0.018027；The frequency spectrum function expression formula of Nuttall window are as follows:
W in formulaR(w) frequency spectrum function of rectangular window, expression formula are indicated are as follows:
Step S3: will add the data sequence after single Nuttall window to carry out periodic extension in the original location, and by the number after continuation
According to longitudinal arrangement after displacement, each row element is made of adjacent N number of Data extension, and adjacent row element moves one compared with lastrow,
N row is formed altogether；
Step S4: weighting the sequence after carrying out periodic extension with 43 rank Nuttall windows again in the vertical direction, and
Longitudinal summation is carried out, the periodic sequence of new N number of data is obtained, completes all phase preprocessing process.Obtained new sequence conduct
The list entries of Fast Fourier Transform (FFT) FFT；
Step S5: the periodic sequence of N number of data pretreated to all phase carries out Fast Fourier Transform (FFT), obtains corresponding
Frequency, phase and amplitude output as a result, complete Nuttall double window all phase detection；In testing result, if main spectral line is k, obtain
It is to main spectral line phase angleObtaining main spectral line amplitude is YN(k)；
Step S6: the resulting testing result of step S5 is corrected by FFT/apFFT phase difference correction method, is adopted
The actual phase of sample signal, amplitude and frequency information.
In an embodiment of the present invention, the step S6 specifically includes following steps,
Step S61: taking the top n point of the primary data of 2N-1 point in step S2 to be directly Fast Fourier Transform (FFT) FFT,
If main spectral line is k, obtaining main spectral line phase angle isObtaining main spectral line amplitude is XN(k)；
Step S62: since all phase Fourier algorithm has the good characteristic of phase invariant, therefore phase estimation can be direct
Take its main spectral line phase angle i.e.:
There are following relationships for the modulus value of the main spectral line amplitude of step S63:FFT and apFFT algorithm:
In formula, Fg(ω) is the spectrum expression formula of window function, and △ ω is resolution ratio △ ω=2 π/N of digital angular frequency；
Then Amplitude Estimation are as follows:
The main spectral line phase angle difference of step S64:FFT and apFFT algorithm exists:
Relationship, τ is group delay coefficient in formula, above-mentioned to show: on frequency deviation value d ω=f-k △ ω and traditional FFT and apFFT main spectral line
The proportional relationship of phase angle difference, proportionality coefficient τ=(1-1/N) π；Then Frequency Estimation are as follows:
Compared to the prior art, the invention has the following advantages:
1, by Nuttall window in conjunction with all phase FFT spectrum analysis technology, both comprehensive advantage not only further reduces inspection
The spectrum leakage of method of determining and calculating also substantially increases algorithm to the precision of phase-detection；
2, inner link existing for traditional FFT and apFFT is utilized, by FFT/apFFT phase difference correction method to double
Nuttall window all phase Fourier algorithm testing result is corrected, and this method physical significance is clear, and the derivation of equation is simply easy
Understand, and calibration result is preferable, and avoids the derivation of equation of conventional correction algorithm complexity；
3, in the case where electric harmonic complexity, especially containing the m-Acetyl chlorophosphonazo being affected by spectrum leakage when, algorithm
Using can also have higher measurement accuracy and reliability.
Detailed description of the invention
Fig. 1 is flow chart of the method for the present invention.
Fig. 2 is all phase pretreatment process figure.
Fig. 3 is that 43 rank Nuttall window Hanning, Blackman windows normalization logarithmic spectrums compare.
Fig. 4 is the present invention compared with other several algorithm measurement amplitude errors.
Fig. 5 is the present invention compared with other several algorithm measurement phase errors.
Specific embodiment
With reference to the accompanying drawing, technical solution of the present invention is specifically described.
A kind of harmonic wave harmonic detection method based on Nuttall double window whole phase FFT of the invention, will have phase not
Become the method for all phase FFT spectrum analysis of characteristic and good spectrum leakage inhibition function, the Nuttall window knot good with sidelobe performance
It closes, contacting between traditional FFT algorithm and all phase Fourier algorithm apFFT is utilized afterwards, using FFT/apFFT phase difference correction
Method is corrected the amplitude and frequency of detection, realizes the detection of Harmonious Waves in Power Systems m-Acetyl chlorophosphonazo；This method implements step
It is as follows,
Step S1: acquiring the signal analyzed from power grid, if the discrete-time signal containing harmonic wave that sampling obtains
Are as follows:
In formula: h is overtone order, and H is highest subharmonic, f1For fundamental frequency, fsFor sample frequency, such as sampling thheorem institute
It states: twice of highest frequency component in the presence of sample frequency is higher than signal in value, Ah、θhRespectively h subharmonic
Virtual value and phase angle；
Step S2: it is collected to upper step as a result, take the primary data of 2N-1 point, by 43 rank Nuttall windows into
The first weighting of row, Nuttall window is as a kind of cosine combination window, time-domain expression are as follows:
In formula: M is the item number of window function；N=0,1,2 ..., N-1；bmConstraint condition should be met, For 43 rank Nuttall windows, b0-b3Take 0.338946 respectively, 0.481973,0.161054,
0.018027；The frequency spectrum function expression formula of Nuttall window are as follows:
W in formulaR(w) frequency spectrum function of rectangular window, expression formula are indicated are as follows:
Step S3: will add the data sequence after single Nuttall window to carry out periodic extension in the original location, and by the number after continuation
According to longitudinal arrangement after displacement, each row element is made of adjacent N number of Data extension, and adjacent row element moves one compared with lastrow,
N row is formed altogether；
Step S4: weighting the sequence after carrying out periodic extension with 43 rank Nuttall windows again in the vertical direction, and
Longitudinal summation is carried out, the periodic sequence of new N number of data is obtained, completes all phase preprocessing process.Obtained new sequence conduct
The list entries of Fast Fourier Transform (FFT) FFT；
Step S5: the periodic sequence of N number of data pretreated to all phase carries out Fast Fourier Transform (FFT), obtains corresponding
Frequency, phase and amplitude output as a result, complete Nuttall double window all phase detection；In testing result, if main spectral line is k, obtain
It is to main spectral line phase angleObtaining main spectral line amplitude is YN(k)；
Step S6: the resulting testing result of step S5 is corrected by FFT/apFFT phase difference correction method, is adopted
The actual phase of sample signal, amplitude and frequency information；Specifically include following steps,
Step S61: taking the top n point of the primary data of 2N-1 point in step S2 to be directly Fast Fourier Transform (FFT) FFT,
If main spectral line is k, obtaining main spectral line phase angle isObtaining main spectral line amplitude is XN(k)；
Step S62: since all phase Fourier algorithm has the good characteristic of phase invariant, therefore phase estimation can be direct
Take its main spectral line phase angle i.e.:
There are following relationships for the modulus value of the main spectral line amplitude of step S63:FFT and apFFT algorithm:
In formula, Fg(ω) is the spectrum expression formula of window function, and △ ω is resolution ratio △ ω=2 π/N of digital angular frequency；
Then Amplitude Estimation are as follows:
The main spectral line phase angle difference of step S64:FFT and apFFT algorithm exists:
Relationship, τ is group delay coefficient in formula, above-mentioned to show: on frequency deviation value d ω=f-k △ ω and traditional FFT and apFFT main spectral line
The proportional relationship of phase angle difference, proportionality coefficient τ=(1-1/N) π；Then Frequency Estimation are as follows:
The following are specific implementation process of the invention.
As shown in Figure 1, a kind of harmonic wave harmonic detection method based on Nuttall double window whole phase FFT of the present invention, including
Following steps:
Step S1: acquiring the signal analyzed from power grid, if the discrete-time signal containing harmonic wave that sampling obtains
Are as follows:
In formula: h is overtone order, and H is highest subharmonic, f1For fundamental frequency, fsFor sample frequency, such as sampling thheorem institute
It states: twice of highest frequency component in the presence of sample frequency is higher than signal in value, Ah、θhRespectively h subharmonic
Virtual value and phase angle；
As shown in Fig. 2, carry out needing to carry out all phase pretreatment, including step S2 to sampled data when all phase analysis,
S3, S4:
Step S2: it is collected to upper step as a result, take the primary data of 2N-1 point, by 43 rank Nuttall windows into
The first weighting of row, Nuttall window is as a kind of cosine combination window, time-domain expression are as follows:
In formula: M is the item number of window function；N=0,1,2 ..., N-1；bmConstraint condition should be met, For 43 rank Nuttall windows, b0-b3Take 0.338946 respectively, 0.481973,0.161054,
0.018027；The frequency spectrum function expression formula of Nuttall window are as follows:
W in formulaR(w) frequency spectrum function of rectangular window, expression formula are indicated are as follows:
Step S3: will add the data sequence after single Nuttall window to carry out periodic extension in the original location, and by the number after continuation
According to longitudinal arrangement after displacement, each row element is made of adjacent N number of Data extension, and adjacent row element moves one compared with lastrow,
N row is formed altogether；
Step S4: weighting the sequence after carrying out periodic extension with 43 rank Nuttall windows again in the vertical direction, and
Longitudinal summation is carried out, the periodic sequence of new N number of data is obtained, completes all phase preprocessing process.Obtained new sequence conduct
The list entries of Fast Fourier Transform (FFT) FFT；
Step S5: the periodic sequence of N number of data pretreated to all phase carries out Fast Fourier Transform (FFT), obtains corresponding
Frequency, phase and amplitude output as a result, complete Nuttall double window all phase detection；In testing result, if main spectral line is k, obtain
It is to main spectral line phase angleObtaining main spectral line amplitude is YN(k)；
Step S6: the resulting testing result of step S5 is corrected by FFT/apFFT phase difference correction method, is adopted
The actual phase of sample signal, amplitude and frequency information.
Further, the step S6 specifically includes the following steps:
Step S61: taking the top n point of the primary data of 2N-1 point in step S2 to be directly Fast Fourier Transform (FFT) FFT,
If main spectral line is k, obtaining main spectral line phase angle isObtaining main spectral line amplitude is XN(k)；
Step S62: since all phase Fourier algorithm has the good characteristic of phase invariant, therefore phase estimation can be direct
Take its main spectral line phase angle i.e.:
There are following relationships for the modulus value of the main spectral line amplitude of step S63:FFT and apFFT algorithm:
In formula, Fg(ω) is the spectrum expression formula of window function, and △ ω is resolution ratio △ ω=2 π/N of digital angular frequency.
Then Amplitude Estimation are as follows:
The main spectral line phase angle difference of step S64:FFT and apFFT algorithm exists:
Relationship, τ is group delay coefficient in formula, above-mentioned to show: on frequency deviation value d ω=f-k △ ω and traditional FFT and apFFT main spectral line
The proportional relationship of phase angle difference, proportionality coefficient τ=(1-1/N) π.Then Frequency Estimation are as follows:
Fig. 3 compares the normalization logarithmic spectrum of 43 rank Nuttall window Hanning, Blackman windows, it can be seen that
Window function side lobe peak of the present invention is low, and side lobe attenuation rate is fast, and valve characteristic has a clear superiority.Fig. 4, Fig. 5 are compared
Inventive algorithm and other application conditions of a few quasi-tradition algorithms in amplitude and phase measurement, it can be seen that using this hair
Bright technical solution has higher precision and reliability.
The above are preferred embodiments of the present invention, all any changes made according to the technical solution of the present invention, and generated function is made
When with range without departing from technical solution of the present invention, all belong to the scope of protection of the present invention.
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